Machines for producing transverse images of body sections by the methods of computed tomography are known, for example, for U.S. Pat. Nos. 3,778,614 and 3,924,129 which are incorporated herein, by reference, as background material. In such apparatus one or more beams of penetrating radiation, typically X-rays, are projected through the body in a plurality of directions and are measured, typically with electronic radiation detectors, to yield a multiplicity of projections of internal body structures. The projections are then combined typically in a digital computer using, for example, a convolution-backprojection technique, to generate images of transverse sections through the body.
Early methods for computing the transverse image from its projections generally assumed a linear relationship between the lengths of the various constituents and the total attentuation of these constituents so that the integrated tissue density along the path was equal to the logarithm of the ratio of the radiation intensity entering and exiting the body. This assumption, although generally true for a monochromatic radiation source, produces aberrated images if utilized in a scanner having a polychromatic radiation spectrum in conjunction with body constituents having attenuation coefficients which vary with radiation energy. Prior art scanners have included filters for hardening the X-ray beam (to reduce its low energy spectral content) to partially eliminate polychromatic effects. Many prior art scanners have also attempted to compensate for polychromatic effects by effectively assuming a single attenuation function for all body tissues and applying that function, in conjunction with a known spectrum from the X-ray source, as a first order compensation in the image reconstruction calculations (single spectrum or one dimensional corrections).
Virtually all human body tissues are found to have energy dependent X-ray attenuation characteristics which are dominated by the characteristics of water (soft tissues) and bone and can be approximated by a combination of these characteristics. The energy attenuation spectra of water and bone are, however, substantially different. A polychromatic radiation beam propagating through a body which comprises a mixture of bone and soft tissue (on either a macroscopic or microscopic level) will necessarily be influenced by the combined spectra of calcium and water, which interact in a non-linear fashion to distort X-ray intensity values in the measured projections.